Calculus of Variations and Geometric Measure Theory
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M. Goldman - M. Novaga

Volume-constrained minimizers for the prescribed curvature problem in periodic media

created by novaga on 24 Jan 2011
modified on 10 Nov 2018


Published Paper

Inserted: 24 jan 2011
Last Updated: 10 nov 2018

Journal: Calc. Var. and PDE
Volume: 44
Number: 3-4
Pages: 297-318
Year: 2012

ArXiv: 1103.5161 PDF

In this version the statement of Lemma 2.5 has been corrected with respect to the published version.


We establish existence of compact minimizers of the prescribed mean curvature problem with volume constraint in periodic media. As a consequence, we construct compact approximate solutions to the prescribed mean curvature equation. We also show convergence after rescaling of the volume-constrained minimizers towards a suitable Wulff Shape, when the volume tends to infinity.


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